1. Field of the Invention
This invention relates generally to receivers and, more specifically, to receivers that use closed-form parametric estimates of the channel and/or received signal probability density function.
2. Description of the Related Art
In many situations, receiver performance depends on knowledge about the received signal and/or the channel over which the signal has propagated. For example, in the case of intensity-modulation/direct-detection (IM/DD) optical-transmission systems at speeds of 10 Gb/s and higher, chromatic dispersion and polarization-mode dispersion have become major factors that limit the reach of these systems. Electronic dispersion compensation (EDC) is an increasingly popular approach to mitigate these impairments and a cost-effective alternative to purely optical-dispersion-compensation techniques.
Among EDC techniques, maximum-likelihood sequence estimation (MLSE) is a promising approach. MLSE chooses the sequence that minimizes the negative logarithm of the likelihood function (i.e., the metric). However, MLSE receivers require knowledge of the statistics of the noisy received signal. Noise in IM/DD optical channels is strongly non-Gaussian and signal dependent. Except in the simplest situations, the pdf of the signal corrupted by noise does not have a closed-form expression. This can lead to difficulties in the implementation of the MLSE receiver.
If the signal pdf is not known a priori by the receiver, it must be estimated based on the received signal. This is a process known as channel-estimation. In an EDC receiver implemented as a monolithic integrated circuit, channel-estimation algorithms typically must be implemented by dedicated hardware. The amount of computational resources that can be devoted to channel-estimation is usually limited by constraints on the chip area and power dissipation. Therefore, finding computationally efficient channel-estimation methods is of paramount importance.
Channel-estimation methods can be parametric or nonparametric. Parametric methods assume that the functional form for the pdf of the signal is known but its parameters are not, whereas nonparametric methods do not assume any knowledge of the pdf. The main difficulty with nonparametric methods is that a large number of samples are needed to obtain accurate estimates. This is particularly problematic in the tail regions of the signal pdf, where it may take an inordinate amount of time to obtain enough samples. For this reason, parametric methods are preferable. However, parameter estimation may be difficult if the functional form assumed for the pdf is cumbersome or does not have a closed-form expression, particularly when the estimation must be done by hardware operating in real time, as in the case of an adaptive EDC receiver.
Thus, there is a need for improved, computationally efficient approaches to channel estimation and receivers that depend on channel-estimation.